Econ 200H: David Reiley
Due Tuesday, 10 October 2006

## Problem Set #3

As before, the following exercises come from the end-of-chapter problems in the Taylor textbook. Recall that in general, I recommend not spending more than about 20 minutes thinking about any single problem. (The extra-credit problems are an exception - I expect them to take longer, but they are an opportunity for those who are interested in learning more.)

1. (10 points) Taylor, problem 8.2.
2. (10 points) Taylor, problem 8.5.
3. (10 points) (This is a rewritten version of Taylor, problem 8.4.) Suppose the firm in problem 3 adds an additional machine, which changes the short-run average-cost curve so that the minimum AC is 10. Does this imply long-run economies of scale, or diseconomies of scale? Explain your answer by sketching what the two different short-run average cost curves might look like.
4. (20 points) Taylor, problem 8.6.
5. (20 points) Taylor, problem 8.7.
6. (10 points) Explain why P=MC in the short-run equilibrium for a perfectly competitive firm, whereas in the long run P=MC=AC.
7. (10 points) If the firm's lowest average cost is \$48 and its lowest average variable cost is \$24, what does it pay a perfectly competitive firm to do if:
1. the market price is \$49?
2. the market price is \$30?
3. the market price is \$8?
8. (10 points) The firm's MC curve goes through the lowest point of its ATC curve and also through the lowest point of its AVC curve. But the AVC curve lies below the AC curve, so how can both of these statements be true? Why are they true?
9. (10 points) Taylor, problem 9.1.
10. (10 points) Taylor, problem 9.4.
11. (5 points) Taylor, problem 9.6.
12. (10 points) Taylor, problem 9.7.
13. (10 points) Taylor, problem 9.8.
14. (20 points) Taylor, problem 9.10.
15. (10 points) Taylor, problem 10.1.
16. (10 points) Taylor, problem 10.4.
17. (10 points) Taylor, problem 10.5.
18. (15 points) Taylor, problem 10.7.
19. (10 points) Taylor, problem 10.9. Note: In this problem you may run into uncertainty because the table only gives values for even numbers of quantity units. Assume that the good in question is something sold in pairs, like shoes, so that you can't sell an odd number.
20. (20 points) Taylor, problem 10.10. Note: there is an error in this problem. In addition to "showing" the loss of consumer surplus and the deadweight loss on your graph, please also compute the values of these amounts.
21. (20 points) In this problem, we will demonstrate the result described in footnote 1 on page 251 of the text. Suppose there is a monopoly seller for chocolate shakes on campus, and she faces the demand curve Q=100-10P.
1. What is the price when the monopolist sells just one shake? Use this information to compute the marginal revenue for the first unit sold.
2. What is the price when the monopolist sells two shakes? Use this information to compute the marginal revenue for the second unit sold.
3. Consider the prices at which the monopolist could sell either 20 or 21 shakes. Use these to compute the marginal revenue for the 21st unit sold.
4. Similarly, compute the marginal revenue for the 22nd unit sold.
5. Similarly, compute the marginal revenue for the 51st unit sold.
6. Plot the demand curve. On this same graph, plot the five points you have computed above. Connect these dots to produce a marginal-revenue curve.
7. What is the equation of this marginal-revenue curve as a function of Q?
Note that, as described in footnote 1, the monopolist is facing a linear demand curve, and therefore the MR curve is also linear, starting at approximately the same price as the demand curve starts when Q=0, and decreasing with twice the slope of the demand curve as Q increases. The reason this is only approximately true is that we're working with discrete instead of continuously divisible units. (One can prove this result, which is true for all linear demand curves, using calculus.)
22. (10 points) Suppose that a monopoly seller of footballs can profitably sell at different prices in two different markets: high school and college. High-school students have perfectly elastic demand at a price of \$4. College students have downward-sloping demand: Q=100-10P.
1. If the monopolist is price-discriminating optimally, what must be true of marginal revenues in the two different markets?
2. Even without knowing the monopolist's cost curves, it is possible in this situation to figure out what the prices should be in the two different markets. You'll need to use the marginal-revenue result from the previous problem. What should the two prices be?
23. (20 points) Visit my Market.Econ Web site. Sign up for an account on the site, and then play at least five 10-period games of the Potato Wafer Game. The total points you earn on this exercise will be determined by the % of cumulative profits you earn, averaged across all games you play. You may play as many games as you like in an effort to raise your average.
24. (Optional - 15 extra-credit points) Read the Appendix to Chapter 8, on Producer Theory with Isoquants, and answer problems 8A.1.-8A.3.
25. (Optional - 20 extra-credit points). Every time you play the Potato Wafer Game, the demand curve has a linear form: Q = a - b P, where a and b are numbers chosen at random. In addition, you face fixed costs of size F and marginal costs of size c per unit produced. (In every game, F = \$2 million, and c = \$0.75.) Your assignment in this extra-credit problem is to derive a formula for the optimal price. Your answer should be an equation that relates the optimal price P* to the parameters a, b, c, and F.

After deriving the correct formula, please indicate how the optimal price changes when a increases, when b increases, when c increases, and when F increases.

(Hint #1: You will want to use calculus to derive this formula.)
(Hint #2: This can be done by referring to what we've learned in the text, but it is easy to become confused about what the "margin" is. Remember that "marginal revenue" is the change in revenue with respect to a change in quantity, not price.)
(Hint #3: It is possible to derive the correct formula without referring to the text, so long as you understand the profit-maximization problem well and know how to use calculus.)
26. (Optional - 10 extra-credit points). Provide evidence of a specific example of price discrimination. (Note that two different firms charging two different prices is not price discrimination. Price discrimination involves a single firm charging different prices to different customers.). Your evidence might be a newspaper article, a couple of online advertisements, or a couple of receipts showing different prices for the same product, for example. Describe what sort of price discrimination is going on, and which type of customer is paying which price.